Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x-3y &= -3 \\ 5x+5y &= 9\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $5y = -5x+9$ Divide both sides by $5$ to isolate $y$ $y = {-x + \dfrac{9}{5}}$ Substitute this expression for $y$ in the first equation. $-6x-3({-x + \dfrac{9}{5}}) = -3$ $-6x + 3x - \dfrac{27}{5} = -3$ Simplify by combining terms, then solve for $x$ $-3x - \dfrac{27}{5} = -3$ $-3x = \dfrac{12}{5}$ $x = -\dfrac{4}{5}$ Substitute $-\dfrac{4}{5}$ for $x$ back into the top equation. $-6( -\dfrac{4}{5})-3y = -3$ $\dfrac{24}{5}-3y = -3$ $-3y = -\dfrac{39}{5}$ $y = \dfrac{13}{5}$ The solution is $\enspace x = -\dfrac{4}{5}, \enspace y = \dfrac{13}{5}$.